A Generating Function Approach to the Enumeration of Matrices in Classical Groups Over Finite Fields (Memoirs of the American Mathematical Society)
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Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.
Introduction, tables, and preliminaries Separable and cyclic matrices in classical groups Semisimple and regular matrices in classical groups Bibliography.
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